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When I shaved in the past with a pre-shave oil, after some time, the oil dried to some degree. But, it was still on the skin. Rewetting made the skin as slippery as before. And, away you go.
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Initially, I used Walmart shave soap, which I suspect is about the same quality as your CVS shave soap. I didn't find it as useless as you do. However, it did dry out more quickly than I would have...